Every polynomial of degree ?$n$? with complex coefficients has exactly ?$n$? roots (counting their multiplicity). Intuitively, it seems to be the case that if the coefficients of a polynomial are slightly altered, their roots will also differ by just a little. It is not entirely obvious, however, how one would prove that, since there is no explicit formula for roots of polynomials of degree four or more. It is also Not obvious, how one would define nearness on a set of roots, which would consider that by changing the coefficients, their multiplicity may also change.

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URN

URN:NBN:SI:doc-VOEJDI7R

COBISSID

150987011

Added

13.02.2025

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Citation

APA:

Ravnikar, Christian (2023). Ničle polinomov so zvezno odvisne od koeficientov polinomov. Matrika, volume 10, issue 1, 8 str. URN:NBN:SI:doc-VOEJDI7R from http://www.dlib.si

MLA:

Ravnikar, Christian. "Ničle polinomov so zvezno odvisne od koeficientov polinomov." Matrika volume 10. issue 1 (2023) 8 str..
<http://www.dlib.si/?URN=URN:NBN:SI:doc-VOEJDI7R>

Matrika
2014-
(Assembly record)